Question

A line passes through the points (1, 4) and (3, –4). Which is the equation of the line?

y = negative 4 x + 8
y = –2x + 6
y = negative one-fourth x + 2
y = 2x + 2

Answer 1

A

Explanation:

Answer 2

The equation of line passing through points (1 , 4) and (3 , - 4) is y = - 4 x + 8

Explanation:

Given as :

A line is passing through points

`x_1` ,
`y_1` = 1 , 4

`x_2` ,
`y_2` = 3 , - 4

Now, Equation of line in point-slope form is

y -
`y_1` = m × (x -
`x_1`)

where m is the slope of line

∵ m =
`(y_2 - y_1)/(x_2 - x_1)`

i.e m =
`( ( - 4 ) - 4)/(3 - 1)`

Or, m =
`( - 8)/(2)`

Or, m = - 4

So, The slope of line = m = - 4

∵, equation of line can be written as

y -
`y_1` = m × (x -
`x_1`)

So, Putting the value of slope, m and points (
`x_1` ,
`y_1` )

i.e y - 4 = ( - 4 ) × ( x - 1 )

Or, y - 4 = ( - 4 ) × x + 4

Or, y - 4 = - 4 x + 4

Or, y = - 4 x + 4 + 4

∴ y = - 4 x + 8

So, The equation of line y = - 4 x + 8

Hence, The equation of line passing through points (1 , 4) and (3 , - 4) is y = - 4 x + 8 Answer